Active Cells: An Exponential Spline Framework for the Interactive Segmentation of Microscopy Images in 2-D and 3-D

M. Unser, R. Delgado

Snakes are effective tools for image segmentation. A snake is a curve that evolves from an initial position towards the boundary of an object in a 2-D image. Its extension to 3-D is an evolving surface. In the literature, these methods are also known as active contours or active surfaces. Their evolution is formulated as an energy minimization problem.

Here, we present a novel parametric design that his targeted towards the segmentation of individual cells. The method relies on exponential splines that are used to build "active cells" which, among other properties, are capable of perfectly reproducing circles and ellipses (resp., spheres and ellipsoids in 3-D), irrespective of their position, size and orientation. The underlying B-spline basis functions (E-splines) are designed to have the shortest possible support to maximize efficiency. Practically this translates into an active cell being specified by a set of E-spline coefficient vectors displayed graphically as a control mesh; the model can be made more or less flexible and allowed to deform almost arbitrarily by increasing the number of control points. The proposed framework is also appropriate for delineating cross sections of cylindrical-like conduits in 2-D, and for outlining any type of blob-like object in 2-D or 3-D, thanks to the ellipse-reproducing property of the E-splines.

Our active cells are implemented in the form of JAVA plugins for ImageJ and Icy. The interface gives the user full control over their shape via the intuitive manipulation of the few control points. The 3-D version is quite unique in its concept, and remarkably fast.